Interpretive Summary: Genomic selection (GS) methods include a number of statistical methods to analyze phenotypes and high density marker data to create models that predict a future phenotype from marker data. Current genomic selection methods only analyze one trait at a time. Genetic correlations between quantitative traits, however, are pervasive in many breeding programs. These correlations indicate that measurements of one trait carry information on another trait. In this study we developed and compared three multi-trait genomic selection methods and compared them on simulated and empirical data. We showed in both simulated and real data that the prediction accuracy for a low heritability trait can be significantly increased (e.g. > 40 percent) when it is correlated with a high heritability trait and the traits are analyzed together using our multi-trait models. Factors affecting the improvement in accuracy were examined by simulation. Results should provide important guides to breeders in their choice of models given their empirical knowledge of traits in their programs.

Technical Abstract:
Genomic selection predicts genetic values with genome-wide markers. It is rapidly emerging in plant breeding and is widely implemented in animal breeding. Genetic correlations between quantitative traits are pervasive in many breeding programs. These correlations indicate that measurements of one trait carry information on another trait. Current univariate genomic selection on a single trait does not take advantage of this information. Multivariate genomic selection on multiple traits could accomplish this but has been little explored and tested in practical breeding programs. In this study, three multivariate linear models (i.e. BLUP, BayesA and BayesCp) were compared using simulated quantitative traits controlled by different genetic architectures. We also contrasted a conventional Bayesian shrinkage method (BayesA) with fixed hyper-parameters wit a full Bayesian modeling with estimated hyper-parametes. We found that optimal priors depended on the genetic architecture of the trait so that estimating them was beneficial. Importantly, we show in both simulated and real breeding data that the prediction accuracy for a low heritability trait can be significantly increased (e.g. > 40 percent) by multivariate genomic selection when a correlated high heritability trait is available. Factors affecting the performance of multiple trait genomic selection were explored. The impacts of multivariate genomic selection on index selection of multiple traits and single trait selection under multiple environments were discussed.